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\section{Method of Generated Solutions}
To overcome limitations of the MES and MMS we developed the Method of Generated Solutions (MGS) \cite{R10}.  
The MGS was designed to verify numerical performance of arbitrary solvers by utilizing exact solutions to given systems of differential and/or
integral equations.  Those exact solutions resemble physical solutions and are generated with the use of splines or some other interpolation and approximation methods.
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With MGS the steps for verifying that equation \ref{eq:maineq} is solved correctly are:

\begin{enumerate}
\item[]
\begin{enumerate}[1.]
\item Obtain an approximate solution {\em u} using a computational tool or by experiment.
\item Approximate or interpolate the data from {\em u} using an appropriate technique (e.g.,
spline interpolation or least-squares approximation). These results, {\em u$_{1}$}, in the
analytical form provide the values at all locations in space and time.
\item Apply the differential operator {\em D} (exact analytical differentiation) to the functions
resulting in step 2. This yields a new function {\em g$_{1}$} and new problem
\begin{equation} \label{eq:maineq2}
Du_{1} = g_{1}
\end{equation}
where exact solution u$_{1}$ and source terms g$_{1}$ are known.
\item Solve equation \ref{eq:maineq2} using the computational tool, and forcing functions g$_{1}$ to get a new solution u$_{2}$.
\item Compare solution u$_{2}$ against exact solution u$_{1}$ (from step 2)
and compute the errors introduced by the solver.
\end{enumerate}
\end{enumerate}

